It's things like this that make it hard to write optimizers where floating point is used. Many algebraic identities just don't apply: x == x can't be reduced to

It's things like this that make it hard to write optimizers where floating point is used. Many algebraic identities just don't apply: x == x can't be reduced to true, 0-x isn't the same as -x (it fails for +0), x<=y isn't the opposite of x>y (because of NaN), (a+b)+c isn't the same as a+(b+c), and you can't replace ac+bc with a*(b+c). The paper "What Every Computer Scientist Should Know About Floating Point Arithmetic" is a good guide to the details.